{"date_published":"2024-02-07T00:00:00Z","article_processing_charge":"No","day":"07","year":"2024","status":"public","date_created":"2024-03-08T10:13:59Z","abstract":[{"lang":"eng","text":"Motivated by applications in the medical sciences, we study finite chromatic\r\nsets in Euclidean space from a topological perspective. Based on the persistent\r\nhomology for images, kernels and cokernels, we design provably stable\r\nhomological quantifiers that describe the geometric micro- and macro-structure\r\nof how the color classes mingle. These can be efficiently computed using\r\nchromatic variants of Delaunay and alpha complexes, and code that does these\r\ncomputations is provided."}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"article_number":"2212.03128","date_updated":"2024-03-20T09:36:56Z","publication":"arXiv","department":[{"_id":"HeEd"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"15094"}]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","main_file_link":[{"url":"https://arxiv.org/abs/2212.03128","open_access":"1"}],"author":[{"id":"34D2A09C-F248-11E8-B48F-1D18A9856A87","last_name":"Cultrera di Montesano","full_name":"Cultrera di Montesano, Sebastiano","first_name":"Sebastiano","orcid":"0000-0001-6249-0832"},{"last_name":"Draganov","id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","first_name":"Ondrej"},{"full_name":"Edelsbrunner, Herbert","first_name":"Herbert","orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","last_name":"Edelsbrunner"},{"first_name":"Morteza","full_name":"Saghafian, Morteza","last_name":"Saghafian","id":"f86f7148-b140-11ec-9577-95435b8df824"}],"language":[{"iso":"eng"}],"publication_status":"submitted","oa":1,"citation":{"short":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).","apa":"Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., &#38; Saghafian, M. (n.d.). Chromatic alpha complexes. <i>arXiv</i>.","ista":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. arXiv, 2212.03128.","ama":"Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic alpha complexes. <i>arXiv</i>.","chicago":"Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Alpha Complexes.” <i>ArXiv</i>, n.d.","mla":"Cultrera di Montesano, Sebastiano, et al. “Chromatic Alpha Complexes.” <i>ArXiv</i>, 2212.03128.","ieee":"S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic alpha complexes,” <i>arXiv</i>. ."},"type":"preprint","oa_version":"Preprint","title":"Chromatic alpha complexes","month":"02","external_id":{"arxiv":["2212.03128"]},"_id":"15091"}